Structural phase transitions of optical patterns in atomic gases with microwave-controlled Rydberg interactions

Abstract

Spontaneous symmetry breaking and formation of self-organized structures in nonlinear systems are intriguing and important phenomena in nature. Advancing such research to new nonlinear optical regimes is of much interest for both fundamental physics and practical applications. Here we propose a scheme to realize optical pattern formation in a cold Rydberg atomic gas via electromagnetically induced transparency. We show that, by coupling two Rydberg states with a microwave field (microwave dressing), the nonlocal Kerr nonlinearity of the Rydberg gas can be enhanced significantly and may be tuned actively. Based on such nonlocal Kerr nonlinearity, we demonstrate that a plane-wave state of probe laser field can undergo a modulation instability (MI) and hence spontaneous symmetry breaking, which may result in the emergence of various self-organized optical patterns. Especially, we find that a hexagonal lattice pattern (which is the only optical pattern when the microwave dressing is absent) may develop into several types of square lattice ones when the microwave dressing is applied; moreover, as a outcome of the MI the formation of nonlocal optical solitons is also possible in the system. Different from earlier studies, the optical patterns and nonlocal optical solitons found here can be flexibly manipulated by adjusting the effective probe-field intensity, nonlocality degree of the Kerr nonlinearity, and the strength of the microwave field. Our work opens a route for versatile controls of self-organizations and structural phase transitions of laser light, which may have potential applications in optical information processing and transmission.

Accessing and manipulating dispersive shock waves in a nonlinear and nonlocal Rydberg medium

“…k cr = [Gρ b /(Rρ b − 1/4)] 1/2 , such that ω becomes imaginary when k > k cr , corresponding to the occurrence of modulation instability (MI). Note that the MI is unique for the defocusing nonlocal medium and crucial for the formation of various optical patterns [74]. In the long wavelength limit (k → 0), the dispersion relation takes the form…”

Self-organized structures of two-component laser fields and their active controls in a cold Rydberg atomic gas

“…Note that, when deriving the above equations, we have assumed that the probe field is a spatial light beam, i.e., its envelopes are stationary (i.e., Ω pj is time-independent everywhere). Such assumption is valid for the probe field having a large time duration, so that a continuous-wave (CW) approximation can be applied [7,8,16]; moreover, the spatial width of the envelopes in z direction is assumed to be large so that a local approximation in the z direction for the effective nonlinear interaction potentials between photons [7,8,14,16] (or called spatial response functions) N jl (r ′ − r) can be made, which gives…”

“…Based on such nonlocality, Sevincli et al [8] showed that a hexagonal optical pattern can spontaneously form through a modulational instability (MI) of plane-wave probe field in a ladder-shaped three-level Rydberg gas (Rydberg-EIT) with repulsive Rydberg-Rydberg interaction. Recently, it was demonstrated that a structural phase transition of optical patterns from a hexagonal lattice to two types of square lattices may occur in an EIT-based Rydberg gas with a microwave dressing between two Rydberg states [16]. These investigations enriched our understanding on the MI and related pattern formation in systems with repulsive (or with both repulsive and attractive) Kerr nonlinearities, which are topics explored in different physical systems by many research groups, from which new pattern formation mechanisms for conservative nonlocal nonlinear systems were found in recent years [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”